Suppose that in a competitive labor market demand for worker

Suppose that in a competitive labor market, demand for workers is Q_D = 10,000 - 100W and the labor supply is Q_S = 2000 + 1900W, where Q is the quantity of workers employed and W is the hourly wage.

a. Suppose that the government imposes a minimum wage of $5 per hour. How many people will be employed under the new minimum wage law?

b. Suppose that the demand for workers changes to Q_D = 14,000 – 100W and the labor supply remains the same. The government still imposes a minimum wage of $5 per hour. How many people will be employed?  

Solution

Equilibrium occurs when demand for labor equals the supply of labor in the factor market.

So,

10000-100W = 2000+1900W

2000W = 10000-2000

W = 8000/2000

W = 4

Quantity of labor Q = 10000-100*4 = 9600

If the wage is set at $5 then

Qs = 2000+1900*5 = 11500

Qd = 10000-100*5 = 9500

There will be surplus labor available in the market. Surplus = Qs - Qd = 11500 - 9500 = 2000

This means that 2000 units of labor will remain unemployed if the minimum wage is set at $5

Now that the Qd changes to Qd = 14000-100W

New Equilibrium,

14000-100W = 2000+1900W

2000W = 12000

W = 6, if the govt still imposes minimum wage of $5 it will not be binding as the market wage is already above the minimum wage.

At W= 6, Q = 14000-100*6 = 13400 labor employed at W=$6